A More Practical Algorithm for Drawing Binary Trees in Linear Area with Arbitrary Aspect Ratio

Garg, Ashim and Rusu, Adrian (2004) A More Practical Algorithm for Drawing Binary Trees in Linear Area with Arbitrary Aspect Ratio. In: Graph Drawing 11th International Symposium, GD 2003, September 21-24, 2003, Perugia, Italy , pp. 159-165 (Official URL: http://dx.doi.org/10.1007/978-3-540-24595-7_15).

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Abstract

Trees are usually drawn using planar straight-line drawings. [1] presented an algorithm for constructing a planar straight-line grid drawing of an n-node binary tree with area O(n) and any pre-specified aspect ratio in the range [n^{-\alpha}, n^{\alpha}], where 0 /le /alpha < 1 is any constant, in time. Unfortunately, the algorithm of [1] is not suitable for practical use. The main problem is that the constant hidden in the "Oh" notation for area is quite large (e.g., it can be as large as 3900). In this paper, we have made several practical improvements to the algorithm, which make it suitable for practical use. We have also conducted experiments on this newer version of the algorithm for randomly-generated and complete binary trees with up to 50,000, and 65,535 nodes, respectively. Our experiments show that it constructs area-efficient drawings in practice, with area at most 10 times and 8 times the number of nodes for randomly-generated and complete binary trees, respectively. Research supported by NSF CAREER Award IIS-9985136, NSF CISE Research Infrastructure Award No. 0101244, and Mark Diamond Research Grant No. 13-Summer-2003 from GSA of The State University of New York.

Item Type:Conference Paper
Additional Information:10.1007/978-3-540-24595-7_15
Classifications:M Methods > M.900 Tree
G Algorithms and Complexity > G.070 Area / Edge Length
P Styles > P.720 Straight-line
ID Code:442

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References

A. Garg and A. Rusu. Straight-line drawings of binary trees with linear area and arbitrary aspect ratio. In Proc. 10th International Symposium on Graph Drawing (GD 2002), volume 2528 of LNCS, pages 320-331. Springer-Verlag, 2002.

A. Garg and A. Rusu. A more practical algorithm for drawing binary trees in linear area with arbitrary aspect ratio. Technical Report No. 2003-12, Department of Computer Science and Engineering, University at Buffalo, Buffalo, NY, 2003.

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